Dude, read Brian Keene's Dead Sea.
One of the BEST zombie novels IMO, and deals exactly with this.

Keene zombies (I've only read The Rising, so I'm going off that) are at least human level smart though, because they're created when demon spirits posses a corpse. Which means they can use tanks. And katanas. And Intercontinental Ballistic Missles. And notice I said corpse, not dead person. In the Keene verse, we could be up against Hind attack helicopters dropping SMART! zombie crocodiles into our compounds.